Complex Networks: Time-Dependent Connections and Silent Nodes

We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of connection weights and, depending on the current degree of order, some connections are reinforced/weakened with strength Phi on short-time scales, and (b) only a fraction rho of nodes are simultaneously active. The resulting dynamics has attractors which, for a range of Phi values and rho exceeding a threshold, become unstable, the instability depending critically on the value of rho. We observe that (i) the activity describes a trajectory in which the close neighborhood of some of the attractors is constantly visited, (ii) the number of attractors visited increases with rho, and (iii) the trajectory may change from regular to chaotic and vice versa as rho is, even slightly modified. Furthermore, (iv) time series show a power-law spectra under conditions in which the attractors space is most efficiently explored. We argue on the possible qualitative relevance of this phenomenology to networks in several natural contexts.

Dynamics and robustness of familiarity memory

When one is presented with an item or a face, one can sometimes have a sense of recognition without being able to recall where or when one has encountered it before. This sense of recognition is known as familiarity. Following previous computational models of familiarity memory we investigate the dynamical properties of familiarity discrimination, and contrast two different familiarity discriminators: one based on the energy of the neural network, and the other based on the time derivative of the energy. We show how the familiarity signal decays after a stimulus is presented, and examine the robustness of the familiarity discriminator in the presence of random fluctuations in neural activity. For both discriminators we establish, via a combined method of signal-to-noise ratio and mean field analysis, how the maximum number of successfully discriminated stimuli depends on the noise level.